A study was conducted to determine whether women who do not have health insurance coverage are less likely to be screened for breast cancer, and whether their disease is more advanced at the time of diagnosis. The medical records for a sample of women who were privately insured and for a sample who were uninsured were examined. The stage of breast cancer diagnosis was assigned a number between 1 and 5, where the 1 denotes the least advanced disease and 5 the most advanced. The relevant observations are saved in data set called insure; the stage of disease is saved under the variable name stage, and an indicator of group status - which takes the value 0 for women who were uninsured and 1 for those who were privately insured - under the name group.

Data set insure; variables stage and group (This data set consists of a large number of repeated observations; rather than display them all, we summarize the outcomes.)

288 Stage 1 and Uninsured

338 Stage 2 and Uninsured

226 Stage 3 and Uninsured

41 Stage 4 and Uninsured

76 Stage 5 and Uninsured

13 Stage 1 and Insured

18 Stage 2 and Insured

34 Stage 3 and Insured

6 Stage 4 and Insured

11 Stage 5 and Insured

a) Could the two-sample t-test be used to analyze these data? Why or why not?

b) Test the null hypothesis to the median stage of cancer for the privately insured women is identical to the median stage of cancer for the uninsured women.